If this is homework, please add the homewok tag. Don't worry, people will still help you.
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Michael Greinecker♦Sep 14 '12 at 9:51

1

But WITHOUT the homework tag, someone will post a complete solution almost instantly. So include the homework tag only if you want help in learning, not merely if you want us to do your work for you.
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GEdgarSep 14 '12 at 14:08

The homework tag was not included, the OP's work was done for them. Ite missa est.
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DidNov 11 '12 at 16:50

How do you know all $Y_{\gamma}$ are $(\sigma\{Y_{\gamma}:\gamma \in C\}$,Borel)-measurable? And why is $X_{n}$, $F_{n}$-measurable??
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Math GirlSep 16 '12 at 19:38

By the very definition of $\sigma\{Y_\gamma: \gamma \in C\} = $ "the smallest $\sigma$-algebra $\Sigma$ such that all $Y_\gamma$ are $(\Sigma, \mathrm{Borel})$-measurable. Same for $F_n$ and $X_n$.
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martiniSep 17 '12 at 9:18